Does the initial distribution of data have any affect on which regularization parameter can work well?

In scenarios when we want to know why performance of a predicting linear regression model when using L1 regularization has outperformed with the case that we have used L2 regularization, I wonder whether the initial distribution of data can have any affect on that?

For example, I have heard that L1 assumes Laplacian prior, while L2 assumes Gaussian prior.

Therefore, does the initial distribution of data have any affect on the regularization parameter we choose?

In general, what can be reasons that one regularization can outperform the other one.

I know that for example, if we want to have sparse data, L1 is usually better. So where are the cases that someone prefers to use L2 regularization?